Why Is My Transparency Shader Not Working
It looks to me that everything works normally, but you have a second material on those faces that doesn't turn transparent (and those faces just happen to form the observed weird shapes due to your mesh).

So to solve this you can either make all faces have the same material or have a transparency node and keyframes for each of those materials.

(If this answer does not work for you, please provide a .blend since other problems might show the same symptoms)

Happy Blending! :)